Indeed, a listener is capable of locating sounds in space with a certain precision, by virtue of the perception of sounds by his two ears. The signals emitted by the sound sources undergo acoustic transformations while propagating up to the ears. These acoustic transformations are characteristic of the acoustic channel that becomes established between a sound source and a point of the individual's auditory canal. Each ear possesses its own acoustic channel, and these acoustic channels depend on the position and the orientation of the source in relation to the listener, the shape of the head and the ear of the listener, and also the acoustic environment (for example reverberation due to a hall effect). These acoustic channels may be modeled by filters commonly called “Head Impulse Responses” or HRIR (for “Head Related Impulse Responses”), or else “Head transfer functions” or HRTF (“Head Related Transfer Functions”) depending on whether a representation thereof is given in the time domain or frequency domain respectively.
With reference to FIG. 1 has been represented a “direct” pathway CD from a source HP1 to the (left) ear OG of the listener AU (viewed from above), this ear OG being situated directly facing the source HP1. Also represented is a “cross” pathway CC between a source HP2 and this same ear OG of the listener AU, the pathway CC passing through the head TET of the listener AU since the source HP2 is disposed on the other side of the mid-plane P with respect to the source HP2.
In an environment without reverberation (for example an anechoic chamber), considering that human faces are symmetric, the HRTF functions for the left ear and for the right ear (termed respectively “left HRTF” and “right HRTF” hereinafter) are identical for the sources which are situated in the mid-plane (plane P which separates the left half from the right half of the body as illustrated in FIG. 2). The acoustic indices utilized by the brain to locate the sounds are often classed into two families of indices:                so-called “monaural” indices relating to the locating of a sound on the basis of a single ear, and        so-called “interaural” indices relating to the locating of a sound by the brain by utilizing the differences between the signals perceived by the left ear and the right ear.        
Known techniques for processing sound data in multi-channel format (for example with more than two loudspeakers) with a view to playback on two loudspeakers only, for example on a headset with a 3D spatialization effect, are described hereinafter.
The term “binaural playback” is then understood to denote listening on a headset to audio contents initially in the multi-channel format (for example in the 5.1 format, or other formats delivering more than two tracks), these audio contents being processed in particular with mixing of the channels so as to deliver only two signals feeding, in the so-called “binaural” configuration, the two mini loudspeakers (or “earpieces”) of a conventional stereophonic headset). Thus, in the transformation from a “multi-channel” format to a “binaural” format, it is sought to offer quality of spatialization and immersion to the headset similar or equivalent to that obtained with a multi-channel playback system comprising as many remote loudspeakers as channels. Furthermore, the term “Transaural® playback” is understood to denote listening on two remote loudspeakers to audio contents initially in a multi-channel format.
Conventionally, for listening to an audio content in the 5.1 multi-channel format on a stereophonic headset or on a pair of loudspeakers, a matrixing of the channels, hereinafter called “sub-mixing” or “Downmix”, is performed. A “Downmix” processing is a matrix processing which makes it possible to pass from N channels to M channels with N>M. It will be considered hereinafter that a “Downmix” processing (provided that it does not take account of spatialization effects) does not involve any filter based on HRTF functions. In general, the matrices of the “Downmix” processing used in sound playback devices (PC computer, DVD player, television, or the like) have constant coefficients which depend neither on time nor frequency. Recent “Downmix” processing procedures now exhibit matrices whose coefficients depend on time and frequency and are adjusted at each instant as a function of a time and frequency representation of the input signals. This type of matrix makes it possible for example to prevent the input signals from cancelling one another out by adding together. A constant-matrix version of a processing of “Downmix” type, termed “Downmix ITU”, has been standardized by the International Telecommunications Union “ITU”. This processing is applied by implementing the following equations:SG=EAVG+Ec*0.707+EARG*0.707SR=EAVD+Ec*0.707+EARD*0.707,
where:                SG and SR are respectively left and right output stereo signals,        EAVG and EAVD are respectively input signals which would have been intended to feed left AVG and right AVD lateral loudspeakers (illustrated in FIG. 2),        EARG and EARD are respectively input signals which would have been intended to feed rear left ARG and rear right ARD loudspeakers, situated behind the listener AU of FIG. 2,        EC is an input signal which would have been intended to feed a central loudspeaker C situated facing the listener AU, and        0.707 represents an approximation of the square root of ½.        
It is possible to consider such gains as gains applied to the loudspeakers.
By way of example, the processing hereinafter termed “Downmix ITU” does not allow the accurate spatial perception of sound events. As indicated previously furthermore, a processing of “Downmix” type, generally, does not allow spatial perception since it does not involve any HRTF filter. The feeling of immersion that the contents can offer in the multi-channel format is then lost with headset listening with respect to listening on a system with more than two loudspeakers (for example in the 5.1 format as illustrated in FIG. 2). By way of example, a sound assumed to be emitted by a mobile source from the front to the rear of the listener, is not played back correctly on a stereo-only system (on a headset with earpieces or a pair of loudspeakers). Furthermore, a sound present solely in the channel SG (or SR) and processed by the “Downmix ITU” sub-mixing is played back only in the left (or right, respectively) earpiece in the case of headset listening, whereas in the case of listening on a system with more than two loudspeakers (for example in the 5.1 format), the right (or left, respectively) ear also perceives a signal by diffraction.
In order to alleviate these drawbacks, the method of sub-mixing to a binaural format, termed “Binaural downmix”, has been developed. It consists in placing virtually five (or more) loudspeakers in a sound environment played back on two tracks only, as if five sources (or more) were to be spatialized for binaural playback. Thus, a content in the multi-channel format is broadcast on “virtual” loudspeakers in a context of binaural playback. The uses of such a technique currently lie mainly in DVD players (on PC computers, on televisions, on living-room DVD players, or the like), and soon on mobile terminals for playing televisual or video data.
In the “Binaural downmix” method, the virtual loudspeakers are created by the so-called “binaural synthesis” technique. This technique consists in applying head acoustic transfer functions (HRTF), to monophonic audio signals, so as to obtain a binaural signal which makes it possible, during headset listening, to have the sensation that the sound sources originate from a particular direction in space. The signal of the right ear is obtained by filtering the monophonic signal with the HRTF function of the right ear and the signal of the left ear is obtained by filtering this same monophonic signal with the HRTF function of the left ear. The resulting binaural signal is then available for headset listening.
This implementation is illustrated in FIG. 3A. A transfer function defined by a filter is associated with each acoustic pathway between an ear of the listener and a virtual loudspeaker (placed as advocated in the 5.1 multi-channel format in the example represented). Thus, with reference to FIG. 3B, for ten acoustic pathways in all:                HCg (respectively HCd) is the filter corresponding to an HRTF for the pathway between the central loudspeaker C and the left OG (respectively right OD) ear of the listener,        HGg (respectively HDd) is the filter corresponding to a so-called “ipsilateral” HRTF (ear “illuminated” by the loudspeaker) for the direct pathway (solid line) between the left lateral AVG (respectively right lateral AVD) loudspeaker and the left OG (respectively right OD) ear of the listener,        HGd (respectively HDg) is the filter corresponding to a so-called “contralateral” HRTF (ear in “the shadow” of the head) for the indirect pathway (dashed lines) between the left lateral AVG (respectively right lateral AVD) loudspeaker and the right OD (respectively left OG) ear of the listener,        HGSg (respectively HDSd) is the filter corresponding to an ipsilateral HRTF for the direct pathway (solid line) between the rear left ARG (respectively rear right ARD) loudspeaker and the left OG (respectively right OD) ear of the listener, and        HGSd (respectively HDSg) is the filter corresponding to a contralateral HRTF for the indirect pathway (dashed line) between the rear left ARG (respectively rear right ARD) loudspeaker and the right OD (respectively left OG) ear of the listener.        
A drawback of this technique is its complexity since it requires two binaural filters per virtual loudspeaker (an ipsilateral HRTF and a contralateral HRTF), therefore ten filters in all in the case of a 5.1 format.
The problem is made more acute when these transfer functions need to be manipulated in the course of various processing procedures such as those according to the MPEG standard and in particular the processing termed “MPEG Surround”®.
Indeed, with reference to point 6.1 1.4.2.2.2 of the document “Information technology—MPEG audio technologies—Part 1: MPEG Surround”, ISO/IEC JTC 1/SC 29 (21 Jul. 2006), a matrix filtering is provided for, in the domain of the sub-bands m (also denoted κ(k) here), of the type:
            H      1              l        ,        k              =                  [                                                            h                11                                  l                  ,                  k                                                                                    h                12                                  l                  ,                  k                                                                                                        h                21                                  l                  ,                  k                                                                                    h                22                                  l                  ,                  k                                                                    ]            =                        [                                                                      h                                      L                    ,                    L                                                        l                    ,                                          κ                      ⁡                                              (                        k                        )                                                                                                                                          h                                      L                    ,                    R                                                        l                    ,                                          κ                      ⁡                                              (                        k                        )                                                                                                                                          h                                      L                    ,                    C                                                        l                    ,                                          κ                      ⁡                                              (                        k                        )                                                                                                                                                                  h                                      R                    ,                    L                                                        l                    ,                                          κ                      ⁡                                              (                        k                        )                                                                                                                                          h                                      R                    ,                    R                                                        l                    ,                                          κ                      ⁡                                              (                        k                        )                                                                                                                                          h                                      R                    ,                    C                                                        l                    ,                                          κ                      ⁡                                              (                        k                        )                                                                                                                          ]                ·                  [                                                    1                                            0                                            0                                            0                                            0                                            0                                                                    0                                            1                                            0                                            0                                            0                                            0                                                                    0                                            0                                            1                                            0                                            0                                            0                                              ]                ·                  w          temp                      l            ,                          κ              ⁡                              (                k                )                                                          ,          ⁢          ⁢      0    ≤    k    <    K    ,      0    ≤    l    <    L  
in order to pass from two monophonic signals to stereophonic signals in binaural representation.
Indeed, this standard provides for an embodiment in which a multi-channel signal is transported in the form of a stereo mixing (downmix) and of spatialization parameters (denoted CLD for “Channel Level Difference”, ICC for “Inter-Channel Coherence”, and CPC for “Channel Prediction Coefficient”). These parameters make it possible in a first step to implement a processing for expanding the stereo mixing (or “downmix”) to three signals L′, R′ and C. In a second step, they allow the expansion of the signals L′, R′ and C so as to obtain signals 5.1 (denoted L, Ls, R, Rs, C and LFE for “Low Frequency Effect”). In the binaural mode, the signals C and LFE are not separate. The signal C is used for the Binaural downmix processing.
Therefore here, three signals (for respective left L′, right R′ and center C′ channels) are firstly constructed on the basis of two monophonic signals. Thus, the notation Wtempl,m; designates a processing matrix for expanding stereo signals to these three channels.
The subsequent processing procedures are thereafter:                a processing for expanding these three channels to N channels in the multi-channel configuration, for example 5 channels in the 5.1 format, and        a processing for spatializing N virtual loudspeakers respectively associated with these N channels so as to obtain a binaural or Transaural®, dual-channel representation, with:        
hL,Cl,m=PL,Cm·e+jφCm/2, for the path from a central loudspeaker associated with the aforementioned channel C to the left ear, hR,Cl,m=PR,Cm·e−jφCm/2, for the path from the loudspeaker associated with the central C to the right ear,
            h              L        ,        L                    l        ,        m              =                                                      (                              σ                L                                  l                  ,                  m                                            )                        2                    ⁢                                    (                              P                                  L                  ,                  L                                m                            )                        2                          +                                            (                              σ                LS                                  l                  ,                  m                                            )                        2                    ⁢                                    (                              P                                  L                  ,                  LS                                m                            )                        2                                ,for the ipsilateral paths to the left ear,
            h              R        ,        L                    l        ,        m              =                  ⅇ                  -                      j            ⁡                          (                                                                    w                    L                                          l                      ,                      m                                                        ⁢                                      ϕ                    L                    m                                                  +                                                      w                    Ls                                          l                      ,                      m                                                        ⁢                                      ϕ                    Ls                    m                                                              )                                          ⁢                                                                  (                                  σ                  L                                      l                    ,                    m                                                  )                            2                        ⁢                                          (                                  P                                      R                    ,                    L                                    m                                )                            2                                +                                                    (                                  σ                  Ls                                      l                    ,                    m                                                  )                            2                        ⁢                                          (                                  P                                      R                    ,                    Ls                                    m                                )                            2                                            ,for the contralateral paths to the left ear,
            h              L        ,        R                    l        ,        m              =                  ⅇ                  j          ⁡                      (                                                            w                  R                                      l                    ,                    m                                                  ⁢                                  ϕ                  R                  m                                            +                                                w                  Rs                                      l                    ,                    m                                                  ⁢                                  ϕ                  Rs                  m                                                      )                              ⁢                                                                  (                                  σ                  R                                      l                    ,                    m                                                  )                            2                        ⁢                                          (                                  P                                      L                    ,                    R                                    m                                )                            2                                +                                                    (                                  σ                  Rs                                      l                    ,                    m                                                  )                            2                        ⁢                                          (                                  P                                      L                    ,                    Rs                                    m                                )                            2                                            ,for the contralateral paths to the right ear,
            h              R        ,        R                    l        ,        m              =                                                      (                              σ                R                                  l                  ,                  m                                            )                        2                    ⁢                                    (                              P                                  R                  ,                  R                                m                            )                        2                          +                                            (                              σ                Rs                                  l                  ,                  m                                            )                        2                    ⁢                                    (                              P                                  R                  ,                  Rs                                m                            )                        2                                ,for the ipsilateral paths to the right ear,
where:                σLl,m and σLsl,m represent relative gains to be applied to the signal of the channel L′ so as to define channels L and Ls respectively of the left direct and left ambience virtual loudspeakers in the 5.1 format, for sample l of frequency band m in time-frequency transform,        σRl,m or σRsl,m relative gains to be applied to the signal of the channel R′ to define channels R and Rs of the right direct and right ambience virtual loudspeakers in the 5.1 format, for sample l of frequency band m in time-frequency transform,        φLm, φLsm, φRm and φRsm are phase shifts corresponding to interaural delays, and        wLl,m, wLsl,m, wRl,m and wRsl,m are weightings such that:        
                                          w            L                          l              ,              m                                =                                                                      (                                      σ                    L                                          l                      ,                      m                                                        )                                2                            ⁢                                                (                                      P                                          R                      ,                      L                                        m                                    )                                2                                                                                                          (                                          σ                      L                                              l                        ,                        m                                                              )                                    2                                ⁢                                                      (                                          P                                              R                        ,                        L                                            m                                        )                                    2                                            +                                                                    (                                          σ                      Ls                                              l                        ,                        m                                                              )                                    2                                ⁢                                                      (                                          P                                              R                        ,                        Ls                                            m                                        )                                    2                                                                    ,                                  ⁢                              w            Ls                          l              ,              m                                =                                                                      (                                      σ                    Ls                                          l                      ,                      m                                                        )                                2                            ⁢                                                (                                      P                                          R                      ,                      Ls                                        m                                    )                                2                                                                                                          (                                          σ                      L                                              l                        ,                        m                                                              )                                    2                                ⁢                                                      (                                          P                                              R                        ,                        L                                            m                                        )                                    2                                            +                                                                    (                                          σ                      Ls                                              l                        ,                        m                                                              )                                    2                                ⁢                                                      (                                          P                                              R                        ,                        Ls                                            m                                        )                                    2                                                                    ,                                  ⁢                              w            R                          l              ,              m                                =                                                                      (                                      σ                    R                                          l                      ,                      m                                                        )                                2                            ⁢                                                (                                      P                                          L                      ,                      R                                        m                                    )                                2                                                                                                          (                                          σ                      R                                              l                        ,                        m                                                              )                                    2                                ⁢                                                      (                                          P                                              L                        ,                        R                                            m                                        )                                    2                                            +                                                                    (                                          σ                      Rs                                              l                        ,                        m                                                              )                                    2                                ⁢                                                      (                                          P                                              L                        ,                        Rs                                            m                                        )                                    2                                                                    ,                                  ⁢                              w            Rs                          l              ,              m                                =                                                                                          (                                          σ                      Rs                                              l                        ,                        m                                                              )                                    2                                ⁢                                                      (                                          P                                              L                        ,                        Rs                                            m                                        )                                    2                                                                                                                        (                                              σ                        R                                                  l                          ,                          m                                                                    )                                        2                                    ⁢                                                            (                                              P                                                  L                          ,                          R                                                m                                            )                                        2                                                  +                                                                            (                                              σ                        Rs                                                  l                          ,                          m                                                                    )                                        2                                    ⁢                                                            (                                              P                                                  L                          ,                          Rs                                                m                                            )                                        2                                                                        .                                                          
The following in particular will be adopted:                PL,Cm is the expression for the spectrum of the transfer function of HRTF type for a path between a central loudspeaker in the 5.1 format and the left ear of a listener,        PR,Cm is the expression for the spectrum of the transfer function of HRTF type for a path between a central loudspeaker in the 5.1 format and the right ear of a listener,        PL,Lsm is the expression for the spectrum of the HRTF for a path between a left ambience loudspeaker in the 5.1 format and the left ear,        PR,Lsm is the expression for the spectrum of the HRTF for a path between a left ambience loudspeaker in the 5.1 format and the right ear,        PL,Rsm is the expression for the spectrum of the HRTF for a path between a right ambience loudspeaker in the 5.1 format and the left ear,        PR,Rsm is the expression for the spectrum of the HRTF for a path between a right ambience loudspeaker in the 5.1 format and the right ear,        PL,Rm is the expression for the spectrum of the HRTF for a path between a right loudspeaker in the 5.1 format and the left ear, and        PR,Rm is the expression for the spectrum of the HRTF for a path between a right loudspeaker in the 5.1 format and the right ear,        PL,Lm is the expression for the spectrum of the HRTF for a path between a left loudspeaker in the 5.1 format and the left ear, and        PR,Lm is the expression for the spectrum of the HRTF for a path between a left loudspeaker in the 5.1 format and the right ear.        
In this example, there are thus ten filters associated with the aforementioned HRTF transfer functions for passing from the 5.1 format to a binaural representation. Hence the complexity problem posed by this technique, requiring two binaural filters per virtual loudspeaker (an ipsilateral HRTF and a contralateral HRTF).